6 papers
On the undefinability of pathological Banach spaces
Clovis Hamel, Franklin D. Tall
Motivated by Tsirelson's implicitly defined pathological Banach space, T. Gowers asked whether explicitly defined Banach spaces must include either or some . J. Iovin…
-Theory for Model Theorists
Clovis Hamel, Franklin D. Tall
We present applications of -theory, the branch of general topology concerned with spaces of real-valued continuous functions, to model theory, mostly in the context of continu…
An undecidable extension of Morley's theorem on the number of countable models
Christopher J. Eagle, Clovis Hamel, Sandra Müller +1
We show that Morley's theorem on the number of countable models of a countable first-order theory becomes an undecidable statement when extended to second-order logic. More general…
Model Theory for -theorists
Clovis Hamel, Franklin D. Tall
We survey discrete and continuous model-theoretic notions which have important connections to general topology. We present a self-contained exposition of several interactions betwe…
Pseudocompactness and the Uniform Metastability Principle in Model Theory
Clovis Hamel, Franklin D. Tall
We prove that uniform metastability is equivalent to all closed subspaces being pseudocompact and use this to provide a topological proof of the metatheorem introduced by Caicedo,…
Turing Invariant Sets and the Perfect Set Property
Clovis Hamel, Haim Horowitz, Saharon Shelah
We show that "all Turing invariant sets of reals have the perfect set property" implies that all sets of reals have the perfect set property. We also show that this result…